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CEMC Gauss (Grade 8), 1999

Algebra Difficulty 3.0 AMC 10/12 Find the answer Canada

Raymonde's financial institution publishes a list of service charges as shown in the table. For her first twenty five transactions, she uses Autodebit three times as often as she writes cheques. She also writes as many cheques as she makes cash withdrawals. After her twenty-fifth transaction, she begins to make single transactions. What is the smallest number of transactions she needs to make so that her monthly service charges will exceed the $\$15.95$ 'all-in-one' fee?

(A) $29$ (B) $30$ (C) $27$ (D) $28$ (E) $31$

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